Browsing by Author "Wheeler, M.F."

Now showing 1 - 13 of 13
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    A Parametric Study of Viscous Fingering in Miscible Displacement by Numerical Simulation
    (1987-06) Moissis, D.E.; Miller, C.A.; Wheeler, M.F.
    Numerical simulation is used to study the effects of several parameters on miscible viscous fingering. A miscible flood of a rectangular slab is simulated in two spatial dimensions. The parameters, obtained by the dedimensionalization of the governing equations, are the viscosity ratio, Peclet numbers associated with molecular diffusion, longitudinal dispersion and transverse dispersion and the aspect ratio of the slab. The effects of local permeability variations and the overall heterogeneity of the porous medium are also considered. A finite element modified method of characteristics is used for the solution of the concentration equation, combined with a mixed finite element method for the solution of the pressure equation. This scheme is essentially free of numerical dispersion. The results suggest that the local permeability distribution near the entrance of the porous medium plays an important role in finger generation, while the permeability distribution downstream does not significantly affect fingering. The number of developing fingers and their growth rates depend strongly on the mobility ratio. The aspect ratio of the slab also influences significantly the number of fingers.
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    An Operator-Splitting Method for Advection-Diffusion-Reaction Problems
    (1987-05) Wheeler, M.F.; Dawson, C.N.
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    Characteristic-Galerkin Methods for Contaminant Transport with Non-Equilibrium Adsorption Kinetics
    (1992-08) Dawson, C.N.; van Duijn, C.J.; Wheeler, M.F.
    A procedure based on combining the method of characteristics with a Galerkin finite element method is analyzed for approximating reactive transport in groundwater. In particular, we consider equations modeling contaminant transport with nonlinear, non-equilibrium adsorption reactions. This phenomena gives rise to non-Lipschitz but monotone nonlinearities which complicate the analysis. A physical and mathematical description of the problem under consideration is given, then the numerical method is described and a priori error estimates are derived.
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    Convergence and Material Balance with MMOC-Galerkin
    (1992-09) Chilakapati, A.; Wheeler, M.F.
    A Modified Method of Characteristics (MMOC) combined with Galerkin finite elements has often been used in the past to solve the advection dominated advection-diffusion equation that arises in miscible displacement, transport of soluble contaminants in groundwater and the bioremediation of contaminated aquifers. In this method the hyperbolic part of the equation is treated with characteristics and the remaining elliptic equation is solved with Galerkin finite elements. The right-hand-side in the later procedure is obtained through numerical integration. We demonstrate here that the error associated with this numerical integration is substantial enough to cause large material balance errors and poor convergence, even in the absence of overshoot and undershoot, typical of the Galerkin procedure. One can reduce the error by taking many quadrature points but at the cost of large CPU time. Finer discretization in space a and in time does not guarantee a better solution when the right-hand-side is not computed exactly . An exact integration scheme is implemented in 1-D. This is conservative and obtains theoretical convergence in the absence of overshoot and undershoot.
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    Domain Decomposition and Mixed Finite Element Methods for Elliptic Problems
    (1987-05) Glowinski, R.; Wheeler, M.F.
    In this paper we describe the numerical solution of elliptic problems with nonconstant coefficients by domain decomposition methods based on a mixed formulation and mixed finite element approximations. Two families of conjugate gradient algorithms taking advantage of domain decomposition will be discussed and their performance will be evaluated through numerical experiments, some of them concerning practical situations arising from flow in porous media.
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    Domain Decomposition for Elliptic Partial Differential Equations with Neumann Boundary Conditions
    (1987-05) Gonzalez, Ruth; Wheeler, M.F.
    Discretization of a self-adjoint elliptic partial differential equation by finite differences or finite elements yields a large, sparse, symmetric system of equations, Ax=b. We use the preconditioned conjugate gradient method with domain decomposition to develop an effective, vectorizable preconditioner which is suitable for solving large two-dimensional problems on vector and parallel machines.
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    Mixed Finite Element Methods for Time Dependent Problems: Application to Control
    (1989-09) Dupont, T.; Glowinski, R.; Kinton, W.; Wheeler, M.F.
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    Modeling of in situ Biorestoration of Organic Compounds in Groundwater
    (1990-10) Chiang, C.Y.; Dawson, C.N.; Wheeler, M.F.
    A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results of vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.
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    Numerical Techniques for the Treatment of Quasistatic Solid Viscoelastic Stress Problems
    (1993-01) Shaw, S.; Warby, M.K.; Whiteman, J.R.; Dawson, C.; Wheeler, M.F.
    For quasistatic stress problems two alternative constitutive relationships expressing the stress in a linear viscoelastic solid body as a linear functional of the strain are derived. In conjunction with the equations of equilibrium these form the mathematical models for the stress problems. These models are first discretized in the space domain using a finite element method and semi-discrete error estimates are presented corresponding to each constitutive relationship. Through the use respectively of quadrature rules and finite difference replacements each semi-discrete scheme is fully discretized into the time domain so that two practical algorithms suitable for the numerical stress analysis of linear viscoelastic solids are produced. The semi-discretes estimates are then also extended into the time domain to give spatially H1 error estimates for each alogrithm. The numerical schemes are predicated on exact analytical solutions for a simple model problem, and finally on design data for a real polymerical material.
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    Some Improved Error Estimates for the Modified Method of Characteristics
    (1988-01) Dawson, C.N.; Russell, T.F.; Wheeler, M.F.
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    Three-Dimensional Bioremediation Modeling in Heterogeneous Porous Media
    (1992-04) Wheeler, M.F.; Roberson, K.R.; Chilakapati, Ashokkumar
    Recently Rice University and Pacific Northwest Laboratory (PNL) have begun a collaborative research effort that involves laboratory, field, and simulation work directed toward validating remediation strategies, including both natural and in situ bioremediation at U.S. Department of Energy (DOE) sites such as Hanford. Because of chemical, biological, geologic and physical complexities of modeling these DOE sites, one of the major simulation goals of the project is to formulate and implement accurate and efficient (parallel) algorithms for modeling multiphase/multicomponent flow and reactive transport. In this paper we first describe the physical problem that needs to be modeled. Because of the emergence of concurrent supercomputing, we propose accurate numerical algorithms that are based on operator-splitting in time and domain decomposition iterative techniques. In particular, three characteristic finite element methods and two operator-splitting algorithms are described for advection-diffusion-reaction problems. Three-dimensional bioremediation modeling results in a heterogeneous saturated porous medium are presented.
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    Time-Splitting for Advection-Dominated Parabolic Problems in One Space Variable
    (1987-11) Wheeler, M.F.; Dawson, C.N.; Kinton, Wendy A.